NAG Toolbox

F01 – matrix operations, including inversion

• F01 Introduction
• f01ab – Inverse of real symmetric positive definite matrix using iterative refinement
• nag_matop_real_symm_posdef_inv
• f01ad – Inverse of real symmetric positive definite matrix
• nag_matop_real_symm_posdef_inv_noref
• f01bl – Pseudo-inverse and rank of real m by n matrix (m≥n)
• nag_matop_real_gen_pseudinv
• f01br – LU factorization of real sparse matrix
• nag_matop_real_gen_sparse_lu
• f01bs – LU factorization of real sparse matrix with known sparsity pattern
• nag_matop_real_gen_sparse_lu_reuse
• f01bu – ULDL^TU^T factorization of real symmetric positive definite band matrix
• nag_matop_real_symm_posdef_fac
• f01bv – Reduction to standard form, generalized real symmetric-definite banded eigenproblem
• nag_matop_real_symm_posdef_geneig
• f01ck – Multiplication of real matrices
• nag_matop_real_gen_matmul
• f01cr – Transposition of a real matrix
• nag_matop_real_gen_trans_inplace
• f01ct – Sum or difference of two real matrices, optional scaling and transposition
• nag_matop_real_addsub
• f01cw – Sum or difference of two complex matrices, optional scaling and transposition
• nag_matop_complex_addsub
• f01ec – Real matrix exponential
• nag_matop_real_gen_matrix_exp
• f01ed – Real symmetric matrix exponential
• nag_matop_real_symm_matrix_exp
• f01ef – Function of a real symmetric matrix
• nag_matop_real_symm_matrix_fun
• f01ej – Real matrix logarithm
• nag_matop_real_gen_matrix_log
• f01ek – Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
• nag_matop_real_gen_matrix_fun_std
• f01el – Function of a real matrix (using numerical differentiation)
• nag_matop_real_gen_matrix_fun_num
• f01em – Function of a real matrix (using user-supplied derivatives)
• nag_matop_real_gen_matrix_fun_usd
• f01en – Real matrix square root
• nag_matop_real_gen_matrix_sqrt
• f01ep – Real upper quasi-triangular matrix square root
• nag_matop_real_tri_matrix_sqrt
• f01eq – General power of a real matrix
• nag_matop_real_gen_matrix_pow
• f01fc – Complex matrix exponential
• nag_matop_complex_gen_matrix_exp
• f01fd – Complex Hermitian matrix exponential
• nag_matop_complex_herm_matrix_exp
• f01ff – Function of a complex Hermitian matrix
• nag_matop_complex_herm_matrix_fun
• f01fj – Complex matrix logarithm
• nag_matop_complex_gen_matrix_log
• f01fk – Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
• nag_matop_complex_gen_matrix_fun_std
• f01fl – Function of a complex matrix (using numerical differentiation)
• nag_matop_complex_gen_matrix_fun_num
• f01fm – Function of a complex matrix (using user-supplied derivatives)
• nag_matop_complex_gen_matrix_fun_usd
• f01fn – Complex matrix square root
• nag_matop_complex_gen_matrix_sqrt
• f01fp – Complex upper triangular matrix square root
• nag_matop_complex_tri_matrix_sqrt
• f01fq – General power of a complex matrix
• nag_matop_complex_gen_matrix_pow
• f01ga – Action of a real matrix exponential on a real matrix
• nag_matop_real_gen_matrix_actexp
• f01gb – Action of a real matrix exponential on a real matrix (reverse communication)
• nag_matop_real_gen_matrix_actexp_rcomm
• f01ha – Action of a complex matrix exponential on a complex matrix
• nag_matop_complex_gen_matrix_actexp
• f01hb – Action of a complex matrix exponential on a complex matrix (reverse communication)
• nag_matop_complex_gen_matrix_actexp_rcomm
• f01ja – Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
• nag_matop_real_gen_matrix_cond_std
• f01jb – Condition number for a function of a real matrix (using numerical differentiation)
• nag_matop_real_gen_matrix_cond_num
• f01jc – Condition number for a function of a real matrix (using user-supplied derivatives)
• nag_matop_real_gen_matrix_cond_usd
• f01jd – Condition number for square root of real matrix
• nag_matop_real_gen_matrix_cond_sqrt
• f01je – Condition number for real matrix power
• nag_matop_real_gen_matrix_cond_pow
• f01jf – Fréchet derivative of real matrix power
• nag_matop_real_gen_matrix_frcht_pow
• f01jg – Condition number for real matrix exponential
• nag_matop_real_gen_matrix_cond_exp
• f01jh – Fréchet derivative of real matrix exponential
• nag_matop_real_gen_matrix_frcht_exp
• f01jj – Condition number for real matrix logarithm
• nag_matop_real_gen_matrix_cond_log
• f01jk – Fréchet derivative of real matrix logarithm
• nag_matop_real_gen_matrix_frcht_log
• f01ka – Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
• nag_matop_complex_gen_matrix_cond_std
• f01kb – Condition number for a function of a complex matrix (using numerical differentiation)
• nag_matop_complex_gen_matrix_cond_num
• f01kc – Condition number for a function of a complex matrix (using user-supplied derivatives)
• nag_matop_complex_gen_matrix_cond_usd
• f01kd – Condition number for square root of complex matrix
• nag_matop_complex_gen_matrix_cond_sqrt
• f01ke – Condition number for complex matrix power
• nag_matop_complex_gen_matrix_cond_pow
• f01kf – Fréchet derivative of complex matrix power
• nag_matop_complex_gen_matrix_frcht_pow
• f01kg – Condition number for complex matrix exponential
• nag_matop_complex_gen_matrix_cond_exp
• f01kh – Fréchet derivative of complex matrix exponential
• nag_matop_complex_gen_matrix_frcht_exp
• f01kj – Condition number for complex matrix logarithm
• nag_matop_complex_gen_matrix_cond_log
• f01kk – Fréchet derivative of complex matrix logarithm
• nag_matop_complex_gen_matrix_frcht_log
• f01le – LU factorization of real tridiagonal matrix
• nag_matop_real_gen_tridiag_lu
• f01lh – LU factorization of real almost block diagonal matrix
• nag_matop_real_gen_blkdiag_lu
• f01mc – LDL^T factorization of real symmetric positive definite variable-bandwidth matrix
• nag_matop_real_vband_posdef_fac
• f01qg – RQ factorization of real m by n upper trapezoidal matrix (m≤n)
• nag_matop_real_trapez_rq
• f01qj – RQ factorization of real m by n matrix (m≤n)
• nag_matop_real_gen_rq
• f01qk – Operations with orthogonal matrices, form rows of Q, after RQ factorization by f01qj
• nag_matop_real_gen_rq_formq
• f01rg – RQ factorization of complex m by n upper trapezoidal matrix (m≤n)
• nag_matop_complex_trapez_rq
• f01rj – RQ factorization of complex m by n matrix (m≤n)
• nag_matop_complex_gen_rq
• f01rk – Operations with unitary matrices, form rows of Q, after RQ factorization by f01rj
• nag_matop_complex_gen_rq_formq
• f01va – Copies a real triangular matrix from full format to packed format
• nag_matop_dtrttp
• f01vb – Copies a complex triangular matrix from full format to packed format
• nag_matop_ztrttp
• f01vc – Copies a real triangular matrix from packed format to full format
• nag_matop_dtpttr
• f01vd – Copies a complex triangular matrix from packed format to full format
• nag_matop_ztpttr
• f01ve – Copies a real triangular matrix from full format to Rectangular Full Packed format
• nag_matop_dtrttf
• f01vf – Copies a complex triangular matrix from full format to Rectangular Full Packed format
• nag_matop_ztrttf
• f01vg – Copies a real triangular matrix from Rectangular Full Packed format to full format
• nag_matop_dtfttr
• f01vh – Copies a complex triangular matrix from Rectangular Full Packed format to full format
• nag_matop_ztfttr
• f01vj – Copies a real triangular matrix from packed format to Rectangular Full Packed format
• nag_matop_dtpttf
• f01vk – Copies a complex triangular matrix from packed format to Rectangular Full Packed format
• nag_matop_ztpttf
• f01vl – Copies a real triangular matrix from Rectangular Full Packed format to packed format
• nag_matop_dtfttp
• f01vm – Copies a complex triangular matrix from Rectangular Full Packed format to packed format
• nag_matop_ztfttp
• f01za – Convert real matrix between packed triangular and square storage formats
• nag_matop_real_tri_pack
• f01zb – Convert complex matrix between packed triangular and square storage formats
• nag_matop_complex_tri_pack
• f01zc – Convert real matrix between packed banded and rectangular storage formats
• nag_matop_real_band_pack
• f01zd – Convert complex matrix between packed banded and rectangular storage formats
• nag_matop_complex_band_pack

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F02